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When decisions are made under uncertainty (DMUU), the decision maker either disposes of an interval of possible profits for each alternative (the interval DMUU) or disposes of a discrete set of payoffs for each decision and then the amount of the profit related to a given alternative depends on the state of nature (the scenario DMUU). Existing methods, used to generate the ranking of decisions and applied to the second problem mentioned, take, to a different extent, into consideration how particular profits assigned to alternatives are ordered in the payoff matrix and what the position of a given outcome is in comparison with other outcomes for the same state of nature. The author proposes and describes several alternative procedures that enable connecting the structure of the payoff matrix with the selected decision. These methods are adjusted to the purpose and the nature of the decision maker. They refer to the Savage’s approach, to the maximin joy criterion, to the normalization technique and to some elements used in expected utility maximization and prospect theory.

In this paper, loss-averse consumer behavior during purchase decision-making process in the dual-channel supply chain is modeled. Loss-averse consumers prefer avoiding losses to gain utility with respect to their reference point while purchasing the product. Two product categories are classified: (1) basic product and (2) luxury goods which have lower and higher reference utility to consumers, respectively. The research objective is to determine the optimal price strategy in dual-channel supply chains and discuss the decision behind loss-averse consumers. To model consumers’ valuation of a product, prospect theory is adopted to calculate the demands of each channel. Then, the optimal pricing strategy and the corresponding profits are found out in a Stackelberg game manner. The results encourage manufacturers of basic goods to engage in dual-channel strategy. Effect of “double marginalization” is reduced if consumers are loss-averse in the dual-channel supply chain. Furthermore, the direct channel online contributes larger demand to the manufacturer. However, manufacturers of luxury goods are not suggested for dual-channel strategy because the demand for direct channel online is negligible and the demand for the retail channel remains unchanged. Nevertheless, retailers cannot obtain benefit from dual-channel and as a result, the profit of basic goods retailers will be reduced.

According to the management by objectives (MBO) theory, performance evaluations should take into account the achievement of management objectives (MOs). The most commonly used performance evaluation method — the cross-efficiency evaluation method — seldom considers the role of MOs as a reference point. According to the prospect theory, decision-makers underestimate the benefits that exceed the reference point; they also exaggerate the losses that fall below the reference point. This irrational psychology is more obvious when evaluating the performance evaluation of peers. As such, this paper proposes a cross-efficiency evaluation method based on prospect theory, which takes MOs as a reference point from a peer perspective. First, taking MOs as reference points, a decision-making unit (DMU) chooses a set of weights for each peer, in order to maximize or minimize the prospects of the peer, according to the benevolent or aggressive attitude of the DMU. In order to improve the adaptability of the method, the precise number of MOs is further extended to be an interval number. Finally, the relationship between models, which are based on precise MOs and interval MOs, is illustrated by propositions. Finally, numerical examples are provided to illustrate the applications of the proposed cross-efficiency evaluation method.

Designing efficient algorithms for the large-scale multi-objective problems (LSMOPs) is a very challenging problem currently. To tackle LSMOPs, we first design a new reference points selection strategy to enhance the diversity of algorithms and avoid the algorithm falling into local minima. The strategy selects not only a part of nondominated solutions with the largest crowding distance, but also a part of relatively uniformly distributed solutions as the reference points. In this way, much better diversity and convergence can be obtained. Second, we propose a direction-guided offspring generation strategy, where a type of potential directions is designed to generate the promising solutions which can balance the convergence and diversity of the obtained solutions and improve the effectiveness of the algorithm significantly. Based on the two proposed strategies, we propose a new effective algorithm for LSMOPs. Numerical experiments are executed on two widely used large-scale multi-objective benchmark problem sets with 200, 500 and 1000 decision variables and a comparison with five state-of-the-art algorithms is made. The experimental results show that our proposed algorithm is effective and can obtain significantly better solutions than the compared algorithms.

Unlike previous studies that adopted price as the reference point in this paper we employ the adjusted order imbalance that relates to volume as a reference. We examine the relationship between a firm's characteristics and stock returns. Adjusted order imbalance, including trading direction of stock index and trading volume of individual stock and stock index, is freely and easily obtained by investors in Taiwan. Employing the panel regression model, this paper found prior adjusted order imbalance has a significantly positive relationship with individual stock returns. Additionally, empirical results show that adjusted order imbalance enhances the impacts of the value and size variables.

In this paper, a method based on prospect theory is proposed to solve the multiple attribute decision making (MADM) problem with three formats of attribute aspirations. According to the idea of prospect theory, reference points concerning attributes are first determined. Then, for the three formats of attribute aspirations, the calculation formulae of alternatives' gains/losses concerning attributes are given. By calculating each alternative's gain/loss, a gain–loss matrix is constructed. Further, using the value function from prospect theory and the simple additive weighting method, the overall prospect value of each alternative is calculated. Based on the obtained overall prospect values, a ranking of alternatives can be determined. Finally, a case study is given to illustrate the use of the proposed method.

Background: Palmar tilt and ulnar variance are crucial parameters for evaluating the distal radius. Identifying suitable reference points for these parameters on lateral wrist radiographs remains challenging. The purpose of this study was to establish reference points for measuring palmar tilt and ulnar variance on lateral wrist radiographs and to evaluate the reliability of these two parameters using the newly defined reference points.

Methods: The distal articular surfaces of 25 cadaver radii were marked at four different locations using thin wires. These bones were radiographed and constant landmarks were recorded. The reliability of the palmar tilt and ulnar variance measurements was assessed using the new reference points and two serial measurements recorded by three observers on 27 standardized lateral wrist radiographs.

Results: The reference points for palmar tilt on lateral radiograph were the dorsal and volar end points of the subchondral line. The subchondral line was connected to two of five metaphyseal cortical lines. The reference point for lateral ulnar variance was easily defined on the midpoint of the proximal aspect of the subchondral line. The corresponding posteroanterior central reference point for ulnar variance was at the ulnar corner of the subchondral line. Inter- and intra-observer reliabilities were overall good for the palmar tilt measurements, and excellent for the ulnar variance measurements.

Conclusions: Palmar tilt can be determined accurately with a good understanding of the radiographic landmarks on lateral radiographs, and by addressing the problems caused by ulnar inclination of the articular surface of the distal radius. Lateral wrist radiographs can provide a complete picture of the ulnar border of the radius for measuring ulnar variance.

We survey a number of financial settings linked by the importance of a reference point in the decision making process. For each of them, we discuss how the reference points affect the decisions. We conclude that it is not a coincidence that reference points are essential to many financial settings. Reference points boost the incentives of the individuals, which we argue is the reason why they are so prevalent. Stronger incentives lead to more effort, which leads to higher achievement and the desire for more reference point-based decisions.

This article presents an overview of the recent development on mathematical treatment of behavioural finance, primarily in the setting of continuous-time portfolio choice under the cumulative prospect theory. Financial motivations and mathematical challenges of the problem are highlighted. It is demonstrated that the solutions to the problem have in turn led to new financial and mathematical problems and machineries.